Basic Cardmembers with a Gold, Platinum, or Reserve Delta SkyMiles Credit Card from American Express may check their first bag for free on all Delta and Delta Connection® flights. The benefit applies to up to 9 people traveling in the eligible Cardmembers reservation.
http://www.delta.com/traveling_checkin/baggage/checked/first_bag_free.jsp
You should bring your qualifying Delta Amex card with you on your trip if you plan to do Airline check-in at your WDW resort so they know you get your first bag free.